Scale-free Spatio-temporal Correlations in Conformational Fluctuations of Intrinsically Disordered Proteins

Abstract

The self-assembly of intrinsically disordered proteins (IDPs) into condensed phases and the formation of membrane-less organelles (MLOs) can be considered as the phenomenon of collective behavior. The conformational dynamics of IDPs are essential for their interactions and the formation of a condensed phase. From a physical perspective, collective behavior and the emergence of phase are associated with long-range correlations. Here the conformational dynamics of IDPs and the correlations therein are analyzed, using µs-scale atomistic molecular dynamics (MD) simulations and single-molecule Förster resonance energy transfer (smFRET) experiments. The existence of typical scale-free spatio-temporal correlations in IDP conformational fluctuations is demonstrated. Their conformational evolutions exhibit "1/f noise" power spectra and are accompanied by the appearance of residue domains following a power-law size distribution. Additionally, the motions of residues present scale-free behavioral correlation. These scale-free correlations resemble those in physical systems near critical points, suggesting that IDPs are poised at a critical state. Therefore, IDPs can effectively respond to finite differences in sequence compositions and engender considerable structural heterogeneity which is beneficial for IDP interactions and phase formation.

Keywords: collective behavior; conformational dynamics; critical phenomena; intrinsically disordered proteins; scale‐free correlation.

Figure 1

Large‐scale conformational fluctuations of three typical intrinsically disordered proteins (IDPs). a) Left: The end‐to‐end distance (R_ee ) of FUS‐C. The trajectory shown is one of the ten 1‐µs trajectories. Right: Representative conformations of FUS‐C at different points in the trajectory. The N‐ to C‐ termini are colored from red to blue. Same as in a) for b) LAF‐N and c) TAF‐C.

Figure 2

The 1/ f behavior in IDP conformational dynamics and scale‐invariant residue domains. a) The power spectrum S(f) of the evolution of the end‐to‐end distance. The power spectra of FUS‐C (orange), LAF‐N (blue), and TAF‐C (purple) all show power law forms for more than three frequency orders of magnitude, and they share similar exponents (≈‐1). The dashed reference line is plotted as a visual guide. b) The size distributions of the residue domains. The domain size s is the number of residues contained in each domain. The maximum of the distribution is normalized to one. The size distributions follow power law forms. The exponent of the dashed reference line τ is 1.15. The deviation from the power law in the tail of the distribution is largely attributed to the finite size effect. c) Finite‐size scaling of the domain size distributions. The domain size s is renormalized based on the IDP system size N, i.e., the sequence length. d) Radius of gyration of the domain versus the domain size, illustrating the fractal domain structure.

Figure 3

Correlations between the relative motions of the residues. a) The correlation function C(r) is the average inner product of the relative motions of residue pairs at mutual distance r. The correlation length ξ is defined by the zero crossing, indicated by the black dashed line. The ξ values for the three IDPs are 1.68 nm (FUS‐C; orange), 2.20 nm (LAF‐N; blue), and 2.15 nm (TAF‐C; purple). The inset shows their correlation lengths are ≈75% of the mean R_g . b) Correlation function C(x) with respect to the rescaled variable x = r/ξ.

Figure 4

Structural heterogeneity along the IDP sequence. The domain involvement of the residues along the sequence of a) FUS‐C, b) LAF‐N, and c) TAF‐C. The domain‐prone regions of the sequence are identified as residues 15–39 in FUS‐C, 83–138 in LAF‐N, and 82–150 in TAF‐C (gray‐shaded areas).

Figure 5

Single‐molecule Förster resonance energy transfer experiments confirm the temporal signature of criticality. a) Schematic diagram of the smFRET experiment. IDPs are immobilized on a PEG‐coated glass surface via a biotin‐streptavidin linkage and are labeled with the FRET dye pair Cy3‐Alexa‐647. Total internal reflection fluorescence (TIRF) microscopy is employed to monitor the fluorescence intensity. b) Representative fluorescence and FRET efficiency trajectories as well as the corresponding FRET efficiency histogram for FUS‐C. The mean FRET efficiency values 〈E〉 (blue dashed line) and 〈E〉 _simulation (black dashed line; calculated from simulation results) are also shown in the histogram. c) The estimated power spectrum of FUS‐C (gray area for error bar: mean ± s.d., based on 62 trajectories). d) Representative fluorescence and FRET trajectories with corresponding efficiency histogram and (e) estimated power spectrum (error bar: mean ± s.d., based on 40 trajectories) for LAF‐N.